Digital communications occur between sending and receiving devices over an intermediate communications medium, or “channel” (e.g., a fiber optic cable or insulated copper wires). Each sending device typically transmits symbols at a fixed symbol rate, while each receiving device detects a (potentially corrupted) sequence of symbols and attempts to reconstruct the transmitted data. A “symbol” is a state or significant condition of the channel that persists for a fixed period of time, called a “symbol interval.” A symbol may be, for example, an electrical voltage or current level, an optical power level, a phase value, or a particular frequency or wavelength. A change from one channel state to another is called a symbol transition. Each symbol may represent (i.e., encode) one or more binary bits of the data. Alternatively, the data may be represented by symbol transitions, or by a sequence of two or more symbols.
Many digital communication links use only one bit per symbol; a binary ‘0’ is represented by one symbol (e.g., an electrical voltage or current signal within a first range), and binary ‘1’ by another symbol (e.g., an electrical voltage or current signal within a second range), but higher-order signal constellations are known and frequently used. In 4-level pulse amplitude modulation (PAM4), each symbol interval may carry any one of four symbols, often denoted as −3, −1, +1, and +3. Two binary bits can thus be represented by each symbol.
Channel non-idealities produce dispersion which may cause each symbol to perturb its neighboring symbols, causing intersymbol interference (ISI). ISI can make it difficult for the receiving device to determine which symbols were sent in each interval, particularly when such ISI is combined with additive noise.
To combat noise and ISI, receiving devices may employ various equalization techniques. Linear equalizers generally have to balance between reducing ISI and avoiding noise amplification. Decision Feedback Equalizers (DFE) are often preferred for their ability to combat ISI without inherently requiring noise amplification. As the name suggests, a DFE employs a feedback path to remove ISI effects derived from previously-decided symbols.
A standard textbook implementation of a DFE employs a number of cascaded circuit elements to generate the feedback signal and apply it to the received input signal, all of which must complete their operation in less than one symbol interval. At a symbol interval of 100 picoseconds (for a symbol rate of 10 GSymbol/s), this implementation is challenging with currently available silicon processing technologies. Even data rates around a few gigabits per second can be difficult to achieve due to performance limitations of silicon-based integrated circuits.
Accordingly, certain proposed designs such as those disclosed in U.S. Pat. No. 8,301,036 (“High-speed adaptive decision feedback equalizer”) and U.S. Pat. No. 9,071,479 (“High-speed parallel decision feedback equalizer”) employ alternative implementations that exploit the use of precomputation modules, though in many cases the complexity and power requirements of such modules may be excessive, constituting a dominant fraction (>80%) of the areal and power requirements for the receiving device.